CN108053379A - A kind of DSPI phase extraction methods based on improved variation mode decomposition - Google Patents
A kind of DSPI phase extraction methods based on improved variation mode decomposition Download PDFInfo
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Abstract
The invention discloses a kind of DSPI phase extraction methods based on improved variation mode decomposition, including：DSPI phase diagrams are gathered, the number of the modal components after being decomposed according to the estimation of phase diagram length and width utilizes the optimal mode quantity of orthogonal index extraction；Variation mode decomposition is carried out to DSPI phase diagrams according to optimal mode quantity, obtains a series of mode function component；The histogram of mode function component is calculated, whether the modal components after being decomposed using histogram analysis to noisy component are carried out IVMD decomposition, respectively calculate the histogram of twice decomposition after component, according to histogram obtain noiseless component twice decomposition after comprising noise；Noiseless component after by the noiseless component after twice decomposition and once decomposing is reconstructed, and obtains speckle pattern after noise reduction；The front and rear phase diagram of deformation is calculated using Hilbert method of changing, it is subtracted each other to obtain DSPI phase diagrams, unpacking is carried out to phase and displacement is extracted.This method reduces noise jamming, obtains precise phase information.
Description
Technical Field
The invention relates to the technical field of optical image processing, in particular to a DSPI phase extraction method based on Improved Variational Modal Decomposition (IVMD).
Background
In recent years, with the development of aerospace, various composite materials have been widely used. However, the performance of the components is obviously reduced and the service time is reduced due to the defects of deformation, displacement and the like in the processing, manufacturing and service processes of the composite materials. Therefore, the composite materials need to be detected and evaluated, a scheme is provided for subsequent rush repair, and the healthy operation of aerospace equipment is guaranteed.
Research shows that when the surface of an object irradiated by coherent light is deformed or displaced, the deformation of the object surface is converted into the phase change of speckles on an imaging surface, and the phenomenon is called speckle interference. Digital speckle interference (DSPI) is a non-contact full-field measurement technique that can measure displacement, deformation, surface defects, etc. of composite materials. At present, speckle phase extraction technologies at home and abroad are mainly divided into two types: one is a phase extraction technique based on a single speckle pattern, namely a spatial carrier method, and the other is a phase extraction technique based on a plurality of speckle patterns represented by a phase shift method. Compared with a phase shift method adopting a plurality of speckle patterns, the spatial carrier technology is used for acquiring only one image at a certain time, is less influenced by environmental disturbance and is more suitable for dynamic measurement. The speckle picture is processed by adopting a proper signal processing method, and the method has important significance for improving the measurement precision of the space carrier phase extraction method.
In the process of implementing the invention, the inventor finds that at least the following disadvantages and shortcomings exist in the prior art:
1. the traditional Fourier transform and wavelet transform have no self-adaptability and can not effectively obtain accurate phase information;
2. the empirical mode decomposition process is completely based on the characteristics of the signal, and the basis function does not need to be manually selected, so the method is widely applied, but the method also has some defects, such as: modal aliasing, lack of theoretical support, and the like, and phase information cannot be effectively extracted.
Disclosure of Invention
The invention provides a DSPI phase extraction method based on improved variational modal decomposition, aiming at the low precision of the traditional phase extraction method in DSPI measurement, the IVMD is adopted to process speckle patterns before and after deformation, parameter setting is not needed, the image can be decomposed, noise interference is reduced, and accurate phase information is obtained, which is described in detail as follows:
a DSPI phase extraction method based on improved variational modal decomposition, the method comprising the steps of:
1) collecting a DSPI phase diagram, estimating the number of decomposed modal components according to the length and the width of the phase diagram, and extracting the optimal modal quantity by using an orthogonal index;
2) carrying out variation modal decomposition on the DSPI phase diagram according to the optimal modal quantity to obtain a series of modal function components;
3) calculating a histogram of the modal function component, analyzing whether the decomposed modal component contains noise by using the histogram, continuously carrying out IVMD decomposition on the noise-containing component, respectively calculating the histograms of the components after secondary decomposition, and obtaining a noiseless component after secondary decomposition according to the histogram;
4) reconstructing the noiseless component after the secondary decomposition and the noiseless component after the primary decomposition to obtain a speckle pattern after noise reduction;
5) and calculating phase diagrams before and after deformation by using a Hilbert change method, and subtracting the phase diagrams to obtain a DSPI phase diagram.
6) Unwrapping the phase map and calculating displacement values.
The step 3) is specifically as follows:
calculating a decomposed modal component histogram, wherein if the decomposed modal component histogram conforms to the normal state, the decomposed modal component histogram is a noisy modal component, and otherwise, the decomposed modal component histogram is a noiseless component;
carrying out IVMD decomposition on the noise-containing modal component to obtain a series of components;
and calculating a histogram after the secondary decomposition, and extracting a noise-free component after the secondary decomposition according to the distribution of the histogram.
The step 5) is specifically as follows:
calculating the phase of the speckle pattern after noise reduction by using a Hilbert method;
and subtracting the speckle phases before and after deformation, wherein the subtraction result is a DSPI phase diagram.
The step 1) is specifically as follows:
judging the length and the width of the phase diagram, and calculating the number of modal components by using the length or the width when the length and the width of the phase diagram are equal;
when the length and the width are not equal, firstly, estimating the range of the modal quantity according to the scale, respectively calculating the orthogonality after decomposition, and selecting the corresponding component number when the orthogonality is minimum, namely the optimal modal quantity.
The step 2) is specifically as follows:
defining modal components as finite bandwidths with different center frequencies; constructing a constraint variational equation according to the minimum principle of the sum of bandwidths of different modes;
aiming at a constraint variational equation, introducing an augmented Lagrange function to convert the constraint variational equation into a non-constraint variational equation;
calculating a saddle point of the augmented Lagrange function by adopting a multiplicative operator alternating direction method, namely, an optimal solution of a constraint variational equation;
and continuously updating the center frequency and the modal component, stopping updating when the modal component meets the iteration stop condition, and outputting a series of decomposed modal function components.
The technical scheme provided by the invention has the beneficial effects that:
1. aiming at the characteristic that the mode quantity needs to be set in the decomposition process of the Variational Mode Decomposition (VMD), the invention provides an improved variational mode decomposition method, which can select the optimal mode quantity in a variational frame and process speckle patterns before and after deformation to obtain the inherent mode component;
2. aiming at the noise component contained in the collected speckle pattern, the IVMD is used for decomposing the picture for multiple times, and the noise component is filtered according to whether the histogram of the modal component conforms to the normal distribution or not, so that the filtered speckle pattern is obtained, the signal-to-noise ratio is improved, and the accurate phase information is further improved;
3. the phase extraction method based on IVMD can calculate the DSPI phase diagram in a self-adaptive mode, and avoids the complex parameter setting of the traditional phase method.
Drawings
FIG. 1 is a flow chart of a DSPI phase extraction method based on improved variational modal decomposition;
FIG. 2 is a schematic diagram of a digital speckle interferometry system;
FIG. 3 is a schematic view of a disk under test;
FIG. 4 is a schematic view of speckle patterns collected before and after disc deformation;
fig. 5 is a deformed phase diagram.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
Example 1
A DSPI phase extraction method based on improved variational modal decomposition, see fig. 1, comprising the steps of:
101: collecting a DSPI phase diagram, estimating the number of the decomposed modal components according to the length and the width of the phase diagram, extracting the optimal modal quantity by using an orthogonal index, and performing variation modal decomposition on the DSPI phase diagram according to the number of the decomposed modal components to obtain a series of modal function components;
102: calculating a first histogram of the modal function components, obtaining noisy modal components and noiseless components according to the first histogram, respectively performing IVMD decomposition on each noisy modal component, respectively calculating a second histogram of the decomposed components, and obtaining noiseless components after secondary decomposition according to the second histogram;
103: reconstructing the noiseless component after the secondary decomposition and the noiseless component after the primary decomposition to obtain a speckle pattern after noise reduction;
104: calculating the phase of the speckle pattern after noise reduction by using a Hilbert method, and subtracting the phases before and after speckle deformation to obtain a DSPI phase;
105: and unwrapping the DSPI phase in a row-by-column mode and extracting displacement.
Wherein, the step 101 is specifically as follows:
judging the length and the width of the phase diagram, and calculating the number of modal components by using the length or the width when the length and the width of the phase diagram are equal;
when the length and the width are not equal, firstly, estimating the range of the modal quantity according to the scale, respectively calculating the orthogonality after decomposition, and selecting the corresponding component number when the orthogonality is minimum, namely the optimal modal quantity.
First defining modal components as finite bandwidths with different center frequencies; constructing a constraint variational equation according to the minimum principle of the sum of bandwidths of different modes;
aiming at a constraint variational equation, introducing an augmented Lagrange function to convert the constraint variational equation into a non-constraint variational equation;
calculating a saddle point of the augmented Lagrange function by adopting a multiplicative operator alternating direction method, namely, an optimal solution of a constraint variational equation;
and continuously updating the center frequency and the modal component, stopping updating when the modal component meets the iteration stop condition, and outputting a series of decomposed modal function components.
Further, the step 102 specifically includes:
calculating a histogram of the modal component of the speckle pattern after IVMD decomposition;
analyzing whether the histogram of the modal component conforms to normal distribution or not, wherein if the histogram of the modal component conforms to the normal distribution, the modal component is a noisy component, and otherwise, the modal component is a noiseless component;
and continuously processing the noisy components by using the IVMD, analyzing the decomposed histogram, and extracting the noiseless components after secondary decomposition.
Further, the step 104 specifically includes:
respectively calculating the phase diagrams of the speckle patterns after noise reduction by using a Hilbert method;
and subtracting the phase diagrams before and after deformation to obtain a DSPI phase diagram.
In summary, in the embodiment of the present invention, through the steps 101 to 105, on the premise of a speckle pattern including noise, improved variational modal decomposition is proposed to process the speckle pattern, noise interference is reduced according to a histogram, a phase diagram after noise reduction is calculated by using a hilbert method, and measurement accuracy is improved.
Example 2
The scheme in embodiment 1 is further described below with reference to specific calculation formulas, examples, and fig. 1 to 5, and is described in detail below:
201: a digital speckle interferometry system is built by combining the figure 2, a CCD camera in the digital speckle interferometry system is used for collecting speckle patterns before and after the deformation of a measured disc, and the detailed operation of the step is as follows:
a digital speckle interferometry system is constructed and comprises a CCD camera, an imaging lens, a laser and the like.
The optical path of the measuring system is shown in fig. 2, laser emitted by a laser is divided into two beams by a spectroscope, one beam irradiates the surface of a measured object, the other beam is transmitted along an optical fiber through a coupling lens to serve as object light, diffuse reflected light of the measured object sequentially passes through an optical wave and an imaging lens to form speckle interference with the object light, a speckle pattern is collected by a CCD camera, the material of a panel of a measured disc (see fig. 3) is a copper sheet, and the collected speckle pattern is shown in fig. 4.
The embodiment of the invention does not limit the size of the copper sheet and sets the size according to the requirement in practical application.
202: the number of the modal components after decomposition is set according to the size of the digital speckle interference phase diagram, and the detailed operation of the step is as follows:
1) decomposing any one-dimensional signal, wherein the number of the modal components after decomposition is as follows:
D＝log2L-1
wherein, L is the length of the one-dimensional signal, and D is the number of the modal components after decomposition.
2) Assuming that the size of the DSPI phase diagram is M multiplied by N, and the number of the components after VMD decomposition is K;
and extracting the optimal modal quantity by utilizing the orthogonality index to obtain a proper modal component.
The VMD method determines the frequency center and the bandwidth of the decomposed component by iteratively searching the optimal solution of the variation model in a variation frame, thereby being capable of decomposing the digital speckle phase diagram in a self-adaptive manner.
3) InitializationAnd n ← 0, constructing a variation problem, and correspondingly constraining variation equations as follows:
wherein f (x) is a DSPI phase diagram, uk(x) Obtaining a 2D analytic signal u of a single-side frequency spectrum for a component after 2D signal decomposition, namely an intrinsic mode function, by using Hilbert transformAS,k(x) Its mathematical expression is as follows:
wherein, ω iskα as center frequencykIs a penalty parameter; x is a vector of the picture; k is the number after decomposition; u. ofkAs decomposed components; δ (d)<x,ωk>Is a dirac function; δ (d)<x,ωk,⊥>) Is omegakInverse Fourier transform under frequency band ⊥ inverse Fourier transform, pi<x,ωk>Are parameters.
4) Aiming at the problem of constrained variation, introducing an augmented Lagrange function to convert the problem of constrained variation into the problem of unconstrained variation, wherein the mathematical expression of the augmented Lagrange function is as follows:
wherein the penalty parameter is αkLagrange function multiplier is lambda, lambda (x) is a multiplier function, ▽ is a calculation norm;<.>is a convolution.
5) In order to solve the problem of the optimal solution, a multiplication operator alternating direction method is adopted to calculate the saddle point of the augmented Lagrange function, namely the optimal solution of the constraint variation equation. The alternate update obtains modal components and center frequency mathematical expressions as follows:
wherein i is a parameter and the value range is 1 to k.
6) Updating Lagrange function multiplier lambda.
Wherein,a frequency domain function that is a multiplier; τ is a coefficient;is a function of the frequency domain of f (x),is composed ofIs measured.
7) If it is notAnd ending the circulation, and outputting the modal components, otherwise, continuing the circulation.
Wherein,for the decomposed modal components, ε is an infinitesimally small positive number.
203: calculating a histogram of the component of the speckle pattern after IVMD decomposition, judging whether the modal component contains a noise component according to the histogram, continuing IVMD decomposition on the noise component, calculating the histogram of the component after secondary decomposition, and extracting a secondary noiseless component, wherein the detailed operation of the step is as follows:
1) calculating a histogram of the decomposed components:
h＝imhist(uk(x))
wherein h is a histogram of the decomposed modal component, and imhist is a histogram function for calculating the decomposed component.
2) Calculating a normalized histogram:
where p is the normalized histogram and numel is the total number of pixels of the decomposed components.
3) And analyzing the normalized histogram, and judging whether the normalized histogram accords with normal distribution, wherein the modal component of the histogram, which accords with the normal distribution, is a noisy component, and otherwise, the modal component is a noiseless component.
4) And (4) continuously carrying out IVMD decomposition on the noise-containing modal component, calculating a histogram of the secondarily decomposed component, analyzing the histogram, and selecting a noise-free component according to the distribution of the histogram.
204: calculating the phase of the speckle pattern after noise reduction by using a Hilbert method, and subtracting the phases before and after speckle deformation to obtain a DSPI phase pattern, wherein the detailed operation of the step is as follows:
1) firstly, performing Hilbert transform on a principal component C (x, y) containing deformation information, and obtaining a wrapping phase through arc tangent;
where ψ (x) is the phase, foFor the carrier frequency, Re { } and Im { } represent the real part and the imaginary part, respectively.
2) Subtracting the phases before and after deformation;
δ＝ψ'-ψ
where δ is the DSPI phase, see fig. 5, ψ' is the phase diagram after deformation, ψ is the phase diagram before deformation.
205: the DSPI phase is unfolded (i.e. unwrapped) row by row and column by column, and the displacement is extracted according to the linear relation between the displacement and the phase, and the detailed operation of the step is as follows:
1) and expanding the DSPI phase, wherein the mathematical expression of the phase expansion is as follows:
2) calculating the displacement according to the relation between the phase value and the displacement, wherein the mathematical expression is as follows:
where d is the shift and λ is the wavelength.
In summary, in the embodiment of the present invention, on the premise that the speckle pattern including a large amount of noise is realized through the steps 201 to 205, the IVMD is adopted to perform adaptive decomposition on the speckle pattern, noise interference is filtered according to histogram distribution characteristics, the signal-to-noise ratio of the phase diagram is improved, and accurate phase information is obtained by using the hilbert transform method.
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited, as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (6)
1. A DSPI phase extraction method based on improved variational modal decomposition is characterized by comprising the following steps:
1) collecting a DSPI phase diagram, estimating the number of decomposed modal components according to the length and the width of the phase diagram, and extracting the optimal modal quantity by using an orthogonal index;
2) carrying out variation modal decomposition on the DSPI phase diagram according to the optimal modal quantity to obtain a series of modal function components;
3) calculating a histogram of the modal function component, analyzing whether the decomposed modal component contains noise by using the histogram, continuously carrying out IVMD decomposition on the noise-containing component, respectively calculating the histograms of the components after secondary decomposition, and obtaining a noiseless component after secondary decomposition according to the histogram;
4) reconstructing the noiseless component after the secondary decomposition and the noiseless component after the primary decomposition to obtain a speckle pattern after noise reduction;
5) calculating phase diagrams before and after deformation by using a Hilbert change method, and subtracting the phase diagrams to obtain a DSPI phase diagram;
6) and unwrapping and extracting the displacement of the phase.
2. The DSPI phase extraction method according to claim 1, wherein said step 3) is specifically:
calculating a decomposed modal component histogram, wherein if the decomposed modal component histogram conforms to the normal state, the decomposed modal component histogram is a noisy modal component, and otherwise, the decomposed modal component histogram is a noiseless component;
carrying out IVMD decomposition on the noise-containing modal component to obtain a series of components;
and calculating a histogram after the secondary decomposition, and extracting a noise-free component after the secondary decomposition according to the distribution of the histogram.
3. The DSPI phase extraction method according to claim 1, wherein said step 5) is specifically:
calculating the phase of the speckle pattern after noise reduction by using a Hilbert method;
and subtracting the speckle phases before and after deformation, wherein the subtraction result is a DSPI phase diagram.
4. The DSPI phase extraction method based on improved variational modal decomposition according to claim 1, wherein said step 1) is specifically:
judging the length and the width of the phase diagram, and calculating the number of modal components by using the length or the width when the length and the width of the phase diagram are equal;
when the length and the width are not equal, firstly, estimating the range of the modal quantity according to the scale, respectively calculating the orthogonality after decomposition, and selecting the corresponding component number when the orthogonality is minimum, namely the optimal modal quantity.
5. The DSPI phase extraction method based on improved variational modal decomposition according to claim 1, wherein said step 2) is specifically:
defining modal components as finite bandwidths with different center frequencies; constructing a constraint variational equation according to the minimum principle of the sum of bandwidths of different modes;
aiming at a constraint variational equation, introducing an augmented Lagrange function to convert the constraint variational equation into a non-constraint variational equation;
calculating a saddle point of the augmented Lagrange function by adopting a multiplicative operator alternating direction method, namely, an optimal solution of a constraint variational equation;
and continuously updating the center frequency and the modal component, stopping updating when the modal component meets the iteration stop condition, and outputting a series of decomposed modal function components.
6. The DSPI phase extraction method according to claim 1, wherein the step 6) is specifically:
expanding the subtracted phases by adopting a row-by-row and column-by-column method;
and calculating the displacement according to the linear relation between the expanded phase and the displacement.
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